Heat vegetable oil over medium-high heat in a Dutch oven. Add chicken and bacon; cook and stir until chicken is deep golden brown and bacon is crisp, 5 to 10 minutes. Drain oil, leaving chicken and bacon in Dutch oven.

Pour water into Dutch oven and bring to a boil while scraping the browned bits of food off of the bottom with a wooden spoon.

Stir tomato sauce, green olives, garlic, vermouth, lemon juice, and red pepper flakes into chicken mixture. Reduce heat to medium and, stirring occasionally, simmer until liquid reduces to a thick sauce, about 1 hour.